Tiffany is 3 years older than Nadia. Ten years ago, Tiffany was 4 times as old as Nadia. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Tiffany and Nadia. Let Tiffany's current age be $t$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $t = n + 3$ Ten years ago, Tiffany was $t - 10$ years old, and Nadia was $n - 10$ years old. The information in the second sentence can be expressed in the following equation: $t - 10 = 4(n - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = n + 3$ . Substituting this into our second equation, we get the equation: $(n + 3)$ $-$ $10 = 4(n - 10)$ which combines the information about $n$ from both of our original equations. Simplifying both sides of this equation, we get: $n - 7 = 4 n - 40$ Solving for $n$ , we get: $3 n = 33$ $n = 11$.